Compute-and-Forward on a Multi-User Multi-Relay Channel

TL;DR

This paper proposes an optimized precoding algorithm for a multi-user, multi-relay compute-and-forward system, enhancing the probability of successful message recovery and outperforming standard relaying in specific scenarios.

Contribution

It introduces a novel precoding optimization method to improve linear equation rank and transmission rates in compute-and-forward relay networks.

Findings

Optimized precoding increases full-rank probability.

The scheme outperforms standard relaying in certain regimes.

Numerical results demonstrate the effectiveness of the algorithm.

Abstract

In this paper, we consider a system in which multiple users communicate with a destination with the help of multiple half-duplex relays. Based on the compute-and-forward scheme, each relay, instead of decoding the users' messages, decodes an integer-valued linear combination that relates the transmitted messages. Then, it forwards the linear combination towards the destination. Given these linear combinations, the destination may or may not recover the transmitted messages since the linear combinations are not always full rank. Therefore, we propose an algorithm where we optimize the precoding factor at the users such that the probability that the equations are full rank is increased and that the transmission rate is maximized. We show, through some numerical examples, the effectiveness of our algorithm and the advantage of performing precoding allocation at the users. Also, we show that this scheme can outperform standard relaying techniques in certain regimes.